Rip a hole along the seam of the recliner side in an inconspicuous location, using a seam ripper.
Inspect the contents of the recliner to determine an appropriate stuffing to use. Much furniture produced since 1970 uses foam stuffing, but older furniture may have horsehair or fiber stuffing. Supplement fibrous stuffing with loose polyfill and supplement foam stuffing with foam sheets of a similar density and thickness.
Cut a piece of foam sheeting big enough to puff up the sagging part of the recliner, using a utility knife. Wrap the foam sheeting in cotton batting and insert it into the recliner. Alternatively, stuff loose polyfill into the sagging area to achieve the desired shape and thickness.
Stitch up the ripped recliner side, using an upholstery needle and thread.